复数矢径虚拟边界谱方法在二维空穴声辐射和散射问题中的应用

基于复数矢径虚拟边界积分法，通过将虚拟积分曲线上的未知源强密度函数用Fourier级数展开，同时借助快速数值Fourier变换计算程序，提出了一种求解二维任意形状空穴声辐射和散射问题的复数矢径虚拟边界谱方法．该方法具有以下特点：(1)不存在奇异积分处理；(2)采用复数矢径虚拟边界积分方法，不仅保证了解的唯一性，而且由于虚拟源强密度函数采用Fourier级数展开，克服了用单元离散方法不能用于较高频率范围的缺点；(3)采用快速数值Fourier变换技术使计算效率大幅度提高．文中给出的计算结果表明：在求解任意形状二维空穴声辐射和散射问题上较通常采用的FEM、BEM和VBEM更为有效．

SPECTRUM METHOD OF VIRTUAL BOUNDARY WITH COMPLEX RADIUS VECTOR APPLIED TO ACOUSTIC RADIATION AND SCATTERING PROBLEMS OF 2-D CAVITY OF ARBITRARY SHAPE

Based on the virtual boundary integral method with complex radius vector, and by virtue of expanding the unknown source density distributed on virtual integral curve as Fourier's series, meanwhile combining with the program of the fast Fourier transformation, a spectrum method of virtual boundary with complex radius vector for solving the acoustic radiation and scattering problems of 2-D cavity of arbitrary shape is presented. The advantages of this method are as follows: (1) no singular integral; (2) Adopting the virtual boundary integral method with complex radius vector, not only the uniqueness of solution is ensured, but the shortcoming of the element discretized methods not available in higher-frequency range can be overcome effectually owing to expanding the source density distributed on virtual integral curve as Fourier's series; (3) The efficiency of computation can be improved greatly by means of the program of the fast Fourier transformation. Its numerical results show that the proposed method is more efficient than the FEM BEM and VBEM in common use for solving the acoustic radiation and scattering problems of 2-D cavity with arbitrary shape.